In this paper, a simple yet robust method is proposed for identification of linear continuous time-delay processes from step responses. New linear regression equations are derived from the solution and its various-order integrals of the process differential equation. The regression parameters are then estimated without iterations, and explicit relationship between the regression parameters and those in the process are given. Due to use of the process output integrals in the regression equations, the resulting parameter estimation is very robust in the face of large measurement noise in the output. The proposed method is detailed for a second-order plus dead-time model with one zero, which can approximate most practical industrial processes, covering monotonic or oscillatory dynamics of minimum-phase or non-minimum-phase processes. Such a model can be obtained without any iteration. The effectiveness of the identification method has been demonstrated through simulation and real-time implementation.